Angle facts, parallel lines and polygons worksheet — GCSE Foundation

1.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

2.Which of these describes an obtuse angle?

3.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

4.An angle measures 108°. Write down the name given to an angle of this size.

5.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

6.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

7.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

8.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

9.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

10.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

11.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

12.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

13.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

14.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

15.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.